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Home  >  Volume 25 (2013)

Criterion for Choosing Among Alternative Competitive Models for Assessing the Fit of Regression Models by Osemeke R. F., Efeizomor R.O and Azagbaekwue A. Vol.25 ( Nov. 2013). pp 311-320
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Several statistical measures such as Mallows Cp statistic, coefficient determination r2, adjusted r2, standard error of estimates and forward stepwise regression are used as a criterion for the selection of best subsets regression models in a multiple regression analysis. The best subset fitted models are selected among competitive models based on Cp statistic ≤(P + 1) which means a small biased, the highest value of adjusted r2, highest value of  r2, lowest value of standard error of estimates, low bivariate correlation among the predictors. The predictors X3 (PARKING) and X5 (INCOME) was removed from the model due to non significant effects .The selected best fitted model through studentized residuals (STR) against the predicted value( (y)) ̂  are used to evaluate the aptness of the fitted model .The model X4 (SHOPCNTR) demonstrate some anomalous features and was improve upon by log transformation .The final fitted model was 

Yi = 37.82 – 0.0021X1 – 0.531X2 + 0l0gX4.With iteration method of outlier detention, row 5, row 7 and row 18 of Table 8 was removed from the model because each of the value for standardized residuals is outside the range of 2 x standard deviation or -2 x standard deviation. At each evaluation process, there was a greater improvement in the regression coefficient. The standardized residuals, leverage points, and studentized residuals of Table 8 were used to detect outliers as influential. For studentized residuals, any value that exceed +2(up) and -2(down) are regarded as an outlier. The average leverage value is   P/N , where p is the number of predictors (the number of coefficients plus one for the constant) and n is the sample size. Leverage point greater than (2k+2 )/n  should be carefully examined.